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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 2, Page 256
DOI: https://doi.org/10.7868/S0044466914020069 (Mi zvmmf9990) 		 
This article is cited in 2 scientific papers (total in 2 papers)

$Q$-subdifferential and $Q$-conjugate for global optimality

D. Fortina, I. Tseveendorjb

a INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France
b Laboratoire PRiSM, UMR 8144 Université de Versailles 45, avenue des États-Unis 78035 Versailles Cedex, France
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DOI: https://doi.org/10.7868/S0044466914020069
Abstract: Normal cone and subdifferential have been generalized through various continuous functions; in this article, we focus on a non separable $Q$-subdifferential version. Necessary and sufficient optimality conditions for unconstrained nonconvex problems are revisited accordingly. For inequality constrained problems, $Q$-subdifferential and the lagrangian multipliers, enhanced as continuous functions instead of scalars, allow us to derive new necessary and sufficient optimality conditions. In the same way, the Legendre–Fenchel conjugate is generalized into $Q$-conjugate and global optimality conditions are derived by $Q$-conjugate as well, leading to a tighter inequality.
Key words: global optimality conditions, continuous lagrangian multipliers, subdifferential, Legendre–Fenchel conjugate.
Received: 03.04.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 2, Pages 265–274
DOI: https://doi.org/10.1134/S0965542514020067
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: English
Citation: D. Fortin, I. Tseveendorj, “$Q$-subdifferential and $Q$-conjugate for global optimality”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 256; Comput. Math. Math. Phys., 54:2 (2014), 265–274
Citation in format AMSBIB
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\pages 256
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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